Probing Slow Protein Dynamics by Adiabatic R_1ρ and R_2ρ NMR Experiments

Protein dynamics is central to function. Specifically, conformational dynamics in the μsec-msec timescale is synchronous with phenomena such as allostery, folding, molecular recognition, catalysis and inhibition.^1–11

NMR rotating frame (R_1ρ) and Carr-Purcell-Meiboom-Gill (CPMG, R₂) relaxation dispersion methods have been widely used to probe slow dynamics and discriminate ground and excited states in small and large proteins.^{12, 13} While these approaches have been critical in characterizing enthalpy and entropy in biomolecules, the methods are limited by (a) the small dynamic range of the relaxation dispersion phenomena, (b) difficulty in setting up the pulse sequences, (c) the low tolerance of cryogenic probes for continuous radiofrequency (RF) irradiation, and (d) the cost of performing relaxation measurements at multiple magnetic fields in order to extract reliable dynamic parameters. To expand the dynamic range of relaxation dispersions, sample conditions are often changed (pH, temperature, viscosity, etc.). While there have been some technical improvements to the CPMG method,^{14, 15} there have been no good remedies for the other drawbacks.

In this Communication, we present a conceptually different method for characterizing slow μsec/msec protein motions. Our approach consists of using adiabatic full passage (AFP) pulses¹⁶ to induce a dispersion of relaxation rates, which expands the dynamic range and substantially increases the ease for measuring relaxation dispersion experiments. Unlike the CPMG R₂ or spin-lock R_1ρ dispersion experiments (reviewed in Ref. 17), where relaxation dispersion is obtained by changing the duration between 180° pulses or the spinlocking field strength, we altered the shape of the adiabatic RF irradiation to obtain R_1ρ and R_2ρ dispersion curves. Contrast in relaxation rates can be generated by use of adiabatic RF pulses,¹⁶ which enables the coverage of large bandwidths with relatively low power. While adiabatic pulses have been incorporated in many biomolecular NMR experiments,¹⁸ the concept of using adiabatic RF pulses to induce relaxation dispersion has not been introduced.

We tested this approach with ubiquitin, a globular protein whose dynamics has been recognized to be crucial for proteinprotein recognition.¹⁹ Adiabatic R_1ρ and R_2ρ relaxation rates ^20–22 were measured at 14.1 T (600 MHz ¹H frequency) on a sample of [U-¹⁵N] labeled ubiquitin at 5 °C and 25 °C. A standard 2D HSQC-type pulse sequence (Figure 1)²³ was modified by inserting ¹⁵N pulse trains of 4, 8, 12, 16, 20, 24 and 28 AFP pulses. The relaxation experiments were conducted such that the magnetization rotated in a perpendicular (R_2ρ) direction around the effective field or was aligned with it (R_1ρ). Adiabatic hyperbolic secant (HS) pulses were designed with different “stretching” factors (HSn: n = 1, 2, 4, 6 and 8).²⁴ The applied RF amplitude (ω₁(t)) and frequency sweep (ω_RF(t) - ω_c) of the HSn AFP pulses are:

where ω₁^max is the maximum amplitude of the pulse, β is a truncation factor (sech(β)=0.01), T_p is the length of the AFP pulse, ω_c is the carrier frequency, BW is the bandwidth of the pulse, and t and t′ represent time. Note that ω₁, ω₁^max, ω_RF, ω_c and BW are expressed in units of rad/s. Each AFP pulse was 4-msec and implemented in groups of four (phase-cycled using MLEV-4²⁵), leading to total relaxation delays of 16, 32, 48, 64, 80, 96 and 112 msec (no 112 msec for R_2ρ). The maximum amplitude of the AFP pulse was ω₁^max/(2π) = 3.5 kHz, and the bandwidth, BW/(2π), was 10 kHz. This choice of parameters guaranteed full adiabatic inversion of all residues within a range of ~3 kHz for every HSn pulse. Relaxation rates were obtained in a residue dependent manner by fitting a mono-exponential decay function to the signal intensities versus AFP-train duration. No proton decoupling scheme was used, since net evolution due to heteronuclear scalar coupling was refocused by the ¹⁵N AFP pulses in the R_1ρ and R_2ρ experiments.²⁶

Several relaxation studies have been conducted on ubiquitin, which has a compact fold with nearly all of the residues displaying similar relaxation rates. The relaxation rates measured with our methods (Figure 2) are in agreement with previous data,²⁷ showing essentially constant R_1ρ and R_2ρ rates under each of the HSn pulses. Note that adiabatic pulses cover the entire bandwidth for the ¹⁵N chemical shifts. This avoids the cumbersome back-calculation of the “nominal” effective frequency and tilt angle for each residue of interest, a procedure that requires extremely accurate power calibration when using the spin-lock R_1ρ dispersion approach.

The utilization of different modulation functions induced a dispersion of relaxation rates for all residues, with the smallest adiabatic R_1ρ given by HS1 pulses, followed by HS2, HS4, HS6, and HS8. The opposite trend was seen for R_2ρ. Notably, residues undergoing conformational exchange (e.g., Asn25) exhibited faster adiabatic R_1ρ and R_2ρ and larger dispersions (i.e., the difference in relaxation rates between HS1 and HS8) as compared to residues with no conformational exchange (e.g., Lys48). Residues not undergoing exchange displayed larger R_1ρ dispersion as compared to R_2ρ, while the opposite trend is detected for residues with a contribution from chemical exchange. The dispersion rates become considerably smaller upon increasing the temperature (Figure 2), implying that adiabatic R_1ρ and R_2ρ are mainly sensitive to slow exchange dynamics. Notably, no dispersion of relaxation rates (above 1 Hz) was observed for any residue at 5 °C when measured using the classical CPMG relaxation dispersion method (Figure 3). A small relaxation dispersion was observed in Asn25 using the off-resonance R_1ρ experiment previously used to measure μsec-msec motions in ubiquitin (see Figure 3A).²⁷

Although the complete description of the relaxation during adiabatic pulses would require the evaluation of chemical shift anisotropy, cross-correlated relaxation and interference effects, we assumed that relaxation phenomena not related to chemical exchange are approximately similar across the protein sequence (excluding terminal residues). Under these approximations, the difference of rates between the two kinds of residues represents purely the exchange contribution [e.g., for each HSn pulse: R_{1,2, ρ,ex}=R_1,2ρ(Asn25)-R_1,2ρ(Lys48)]. We analyzed the exchange-induced relaxations during the AFP pulses using the classical formalism developed for the fast exchange regime (1/τ_ex > Δω).^{20, 28, 29} According to this treatment, the R_1ρ and R_2ρ result from an average of instantaneous time-dependent contributions, arising from the inherent time evolution of the effective frequency (ω_eff) and the tilt angle, α, during the pulse:

p_A and p_B are the populations of the two exchanging sites, Δω is the chemical shift difference, and τ_ex is the exchange correlation time. For Asn25 of ubiquitin, the exchange parameters found using Eqs 3 and 4 gave Δω²p_Ap_B = 29 × 10⁴ [rad/s]² and 1/τ_ex ~ 2.5 × 10⁴ s⁻¹, which are in quantitative agreement with the corresponding values reported previously.²⁷

In conclusion, adiabatic rotating frame relaxation measurements, R_1ρ and R_2ρ, provide a solid approach for characterizing μsec-msec protein dynamics. These pulse sequences are straightforward to set-up and implement on any modern spectrometer that can perform phase and amplitude RF modulation. Unlike currently available methods, this approach gives frequency offset independent relaxation rates without the need to apply residue-specific corrections. More importantly, the use of AFP extends the dynamic range of the relaxation dispersion analysis, avoiding troublesome variations of sample conditions and/or use of multiple magnetic field strengths to extract dynamic parameters. The relatively low power utilized for these pulses avoids excess stress to the hardware (probes), and at the same time substantially reduces sample heating. This approach can be applied to a wide range of relaxation measurements from small to large soluble proteins as well as membrane proteins reconstituted in detergent micelles,³⁰ taking advantages of TROSY schemes.³¹ The implementation to other nuclei (¹H, ¹³C, ²H) will be highly beneficial in the characterization of both backbone and side chain dynamics in macromolecular complexes.